Question

prove that √n is not a rational number if n is not a perfect square.​

Answer 1

$let \: \: \sqrt{n \:}$

be rational number

then

$\sqrt{n \: \: } = \frac{p}{q}$

squaring both sides

n=p^2/q^2

nq^2=p^2

therefore n is a factor of p^2

therefore n is a factor of p

let p=n c

nq^2=(nc)^2

q^2=nc^2

therefore n is the factor of q^2

therefore n is the factor of q

But this statement contradicts our assumption

therefore it is irrational

Please mark it as brainliest answer